Why is the hypothesis function $h_{\theta}(x)$ equivalent to $E[y | x; \theta]$ in generalised linear models?
In generalised Linear models, each output variable $y_i$ is modelled as a distribution from the exponential family, with the hypothesis function $h_{\theta}(x)$ for a given $\theta$ as the expected value of $y_i$ and maximum likelihood estimation is usually the method used to solve GLM's.